: A cake recipe calls for 4 cups of flour and 2 cups of sugar.

Mathematics

2 answers:

solong [7]3 years ago

7 0

Answer:

1 cup of sugar per 2 cups of flour

Step-by-step explanation:

Bogdan [553]3 years ago

7 0

I cup of sugar/ 2 cups of flour

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The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.

<h3>How to determine the magnitude and the direction of a resultant</h3>

Vectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:

<h3>Resultant</h3>

$\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)$ (1)

<h3>Magnitude</h3>

$\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}$ (2)

<h3>Direction</h3>

$\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}$ (3)

Where $\theta$ is resultant angle, measured in degrees.

If we know that $\|\vec u\| = 90$ , $\theta_{u} = 40^{\circ}$ , $\|\vec v\| = 60$ , $\theta_{v} = 20^{\circ}$ , $\|\vec w\| = 40$ and $\theta_{w} = 30^{\circ}$ , then the resultant, its magnitude and its direction:

<h3>Resultant</h3>

$\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})$